Best Known (10, 10+122, s)-Nets in Base 4
(10, 10+122, 27)-Net over F4 — Constructive and digital
Digital (10, 132, 27)-net over F4, using
- net from sequence [i] based on digital (10, 26)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 10 and N(F) ≥ 27, using
(10, 10+122, 40)-Net in Base 4 — Upper bound on s
There is no (10, 132, 41)-net in base 4, because
- 13 times m-reduction [i] would yield (10, 119, 41)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4119, 41, S4, 3, 109), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 25 619282 439286 572778 957813 760772 318479 498516 504696 474892 763289 918742 986752 / 55 > 4119 [i]
- extracting embedded OOA [i] would yield OOA(4119, 41, S4, 3, 109), but